Is 7^7/7^x an integer? : GMAT Data Sufficiency (DS)
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# Is 7^7/7^x an integer?

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19 Mar 2010, 18:35
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Is $$\frac{7^7}{7^x}$$ an integer?

(1) $$0\leq{x}\leq{7}$$
(2) $$|x|=x^2$$

(C) 2008 GMAT Club - m04#26

[Reveal] Spoiler:
Statement (1) by itself is insufficient. S1 says that x can be between 0 and 7, so it can be an integer or any fraction.

Statement (2) by itself is sufficient. S2 implies that x is one of (-1, 0, 1). .

WHY CAN THIS BE AN INTEGER OR ANY FRACTION, ISN'T IT ANY INTEGER ALL THE WAY. BECAUSE THE LEAST WHEN X= 7 IS 1 AND X=0 IS 7 * 7*7*7*7*7*7
[Reveal] Spoiler: OA
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Re: Is 7^7/7^x an integer? [#permalink]

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20 Mar 2010, 06:53
aramjung wrote:
Is $$\frac{7^7}{7^x}$$ an integer?

(1) $$0\leq{x}\leq{7}$$
(2) $$|x|=x^2$$

stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.
it cannot be fraction all the way, take for example x = 1/2 it is between 0 to 7 but 7^7/7^1/2 is not an integer
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Re: Is 7^7/7^x an integer? [#permalink]

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20 Mar 2010, 09:37
S1. It is not specified that x is an integer. Using a value such as x=3.5 in the original function will result in a non-integer. Insufficient.
S2. x can only be equal to -1, 0. or 1. Using these values in the original function will always result in an integer. Sufficient.

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Re: Is 7^7/7^x an integer? [#permalink]

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20 Mar 2010, 10:08
1.) x can be any value from 0-7 including decimals. so this is Insuff

2.) using B x= -1, 0, 1, -2, 2.....x is an integer.

Hence B
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Re: Is 7^7/7^x an integer? [#permalink]

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26 Aug 2015, 12:34
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Re: Is 7^7/7^x an integer? [#permalink]

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07 Oct 2015, 02:41
stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.

hii please tell me how do we get just those 3 values for x.
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Re: Is 7^7/7^x an integer? [#permalink]

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07 Oct 2015, 04:35
shreeya wrote:
stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.

hii please tell me how do we get just those 3 values for x.

Square $$|x| = x^2$$:

$$x^2 = x^4$$;

$$x^2 - x^4 = 0$$;

$$x^2(1 - x^2) = 0$$;

$$x^2(1 - x)(1 + x) = 0$$;

$$x = 0$$, $$x = 1$$, or $$x = -1$$.

Hope it's clear.
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Re: Is 7^7/7^x an integer? [#permalink]

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07 Oct 2015, 06:29
yes .. thanks
Re: Is 7^7/7^x an integer?   [#permalink] 07 Oct 2015, 06:29
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